Höher parametrisierte IRT Modelle

Wiederholung

1PL Modell

\[ logit(P(X_{pi}=1)) = \theta_p - \beta_i \] - Logit: Transformation unseres linearen Terms, damit die Werte zwischen 0 und 1 liegen. - Inverse der logit ist die Logistic function.

\[ P(X_{pi}=1) = logistic(\theta_p - \beta_i) \]

1PL exponentielle Form des logistischen Modells

https://www.geo.fu-berlin.de/en/v/soga-r/Basics-of-statistics/Logistic-Regression/The-Logit-Function/index.html \[ P(X_{pi}=1) = \frac{exp(\theta_p - \beta_i)}{1 + exp(\theta_p - \beta_i)} \]

Umschreiben zu

\[ P(X_{pi}=1) = \frac{e^{\theta_p - \beta_i}}{1 + e^{\theta_p - \beta_i}} \]

Vereinfachen

\[ P(X_{pi}=1) = \frac{1}{1 + e^{\color{red}{-}\theta_p \color{red}{+} \beta_i}} \] ## Beispiel

\[ \frac{exp(1 - 0.8)}{1 + exp(1 - 0.8)} = 0.55 \] - \(\theta_p = 1\) - \(\beta_i = 0.8\)

Beispiel

\[ \frac{exp(0.8 - 1)}{1 + exp(0.8 - 1)} = 0.45 \]

\(\theta_p = 0.8\)
\(\beta_i = 1\)

Höher parametrisierte IRT Modelle

Wir können Parameter zu diesem Modell hinzufügen, wodurch wir flexibler in der Modellierung werden:

Schwierigkeit \(\beta_i\) (Intercept)
Steigung \(\alpha\) (Faktorladung, Diskriminationsparameter)
Ratewahrscheinlichkeit \(\gamma_i\) (Guessing probability)

3PL

\[ P(X_{pi}=1) = \gamma_i + (1-\gamma_i)\frac{exp(\alpha_i(\theta_p - \beta_i)))}{1 + exp(\alpha_i(\theta_p - \beta_i))} \] - \(\beta_i\): Schwierigkeit - \(\alpha_i\): discrimination/factor loading/slope - \(\gamma_i\) : guessing probability - Kann entweder geschätzt oder gesetzt werden (z.B. bei 4 Antwortmöglichkeiten: \(\gamma_i = 1/4 = 0.25\)) - Wenn die Lösungswahrscheinlichkeit auf der rehcten Seite sehr gering ist, ist sie immer noch mind. \(\gamma_i\)

2PL

\(\gamma_i = 0\)

\[ P(X_{pi}=1) = \color{red}{0} + (1-\color{red}{0})\frac{exp(\alpha_i(\theta_p - \beta_i)))}{1 + exp(\alpha_i(\theta_p - \beta_i))} \]

Darstellung

viewof alpha1 = Inputs.range(
  [-1, 1], 
  {value: 1, step: .1, label: tex`\alpha_1`}
)
viewof beta1 = Inputs.range(
  [-3, 3], 
  {value: 0, step: .1, label: tex`\beta_1`}
)
viewof alpha2 = Inputs.range(
  [-1, 1], 
  {value: 1, step: .1, label: tex`\alpha_2`}
)
viewof beta2 = Inputs.range(
  [-3, 3], 
  {value: 0, step: .1, label: tex`\beta_2`}
)

line_function = function(alpha, beta, theta) {
    return Math.exp(alpha * (theta - beta)) / (1 + Math.exp(alpha * (theta - beta)));
}

// X-Variable
data = d3.range(-3, 3, 0.1).map((theta) => ({
  x: theta,
  y1: line_function(alpha1, beta1, theta),
  y2: line_function(alpha2, beta2, theta)
}));

Plot.plot(
  {
    x: {grid: false, domain: [-3, 3]}, 
    y: {grid: false, domain: [0, 1]},
    marks: [
      Plot.line(data, {x: "x", y: "y1", stroke: "#9B1B34"}),
      Plot.line(data, {x: "x", y: "y2", stroke: "#99D9DD"}),
    ]
  }
)

1PL

\(\alpha_i = 1\)

\[ P(X_{pi}=1) = 0 + (1-0)\frac{exp(\color{red}{1}(\theta_p - \beta_i)))}{1 + exp(\color{red}{1}(\theta_p - \beta_i))} \]

Simulieren von IRT Daten

Jetzt ist ein guter Zeitpunkt, und uns ein sehr mächtiges Werkzeug anzuschauen: Datensimulation.

Einerseits hilft es hoffentlich, die Konzepte hinter IRT und Linking noch besser zu verstehen.
Hilfreich, z.B. für Poweranalysen

Let’s take a step back!

Geht zur Übung und probiert euch aus!

Welches Modell?

Mögliche Punkte

Gewichtung der Items
Antwortskala
Simulation/Modellfit
Ziel

Exkurs: Tradeoff zwischen
Underfit und
Overfit

Tradeoff zwischen Underfit und Overfit

Tradeoff zwischen Underfit und Overfit

Beurteilung von Fit

z.B.: - lokLikelihood/\(\chi^2\) - AIC, BIC

Was tun bei polytomen Items?

Beispielaufgabe

nie – manchmal – häufig

Wie?

Partial Credit

Grundidee: Den einzelnen Antwortkategorien wird eine eigene Schwierigkeit zugeordnet. Dadurch können wir die Antwortwahrscheinlichkeit in einer bestimmten Kategorie berechnen.

Anwendungsbereich

Ordinale Daten (geordnete Antwortkategorien), z.B.: - Likert-Skalen - Items, die auch mit Teilpunkten bewertet werden können (z.B. Mathe)

Darstellung

Formel

\[ \pi_{pix}= P(X_{pi}=x|\theta_p, \beta_{ik})= \frac{exp[\sum^x_{j=0}(\theta_p-\beta_{ij})]}{1+exp[\sum^k_{j=0}(\theta_p-\beta_{ij})]} \] ::: aside - Person \(p\) - Item \(i\) - Personenscore \(x\) :::

Partial Credit Model

\[ \pi_{pix}= \color{red}{P(X_{pi}=x|\theta_p, \beta_{ik})}= \frac{exp[\sum^x_{j=0}(\theta_p-\beta_{ij})]}{1+exp[\sum^k_{j=0}(\theta_p-\beta_{ij})]} \]

Partial Credit Model

\[ \pi_{pix}= P(X_{pi}=x|\theta_p, \beta_{ik})= \frac{exp[\sum^x_{j=0}\color{red}{(\theta_p-\beta_{ij})}]}{1+exp[\sum^k_{j=0}(\theta_p-\beta_{ij})]} \]

Wichtig:\(/beta_{i\color{red}{j}}\) ist jetzt der Schwellenparameter der Kategorie \(j\) des Items \(i\).

Raw score curve

Übung

Partial Credit Modell fitten.

Grit scale
Oder Psychometrics data und so tun, als ob die das selber ausgefüllt hätten. Und dann auf 5 Stufen kondensieren oder so. Aber was ist hier mit Eindimensionalität? -> Könnte aber einfach ein subset nehmen, die vermutlich eindimensional sind? Achso, und sollte eigentlich ok sein. Die sollten ja nur aufgrund des Konstruktes korrelieren. Aber: Was ist mit missings, haben alle alles bearbeitet?

This is actuallyu quite a comprehensive tutorial.

Hier auch nochmal schauen: https://www.edmeasurementsurveys.com/TAM/Tutorials/5PartialCredit.htm

                              messy_neat disorganized_self.disciplined
messy_neat                     1.0000000                     0.8106662
disorganized_self.disciplined  0.8106662                     1.0000000
ADHD_OCD                       0.7900800                     0.7793043
chaotic_orderly                0.8205825                     0.7954963
lazy_diligent                  0.6354662                     0.7927139
tardy_on.time                  0.8293504                     0.8466559
spontaneous_scheduled          0.7805277                     0.7413686
underachiever_overachiever     0.5842898                     0.6923879
                               ADHD_OCD chaotic_orderly lazy_diligent
messy_neat                    0.7900800       0.8205825     0.6354662
disorganized_self.disciplined 0.7793043       0.7954963     0.7927139
ADHD_OCD                      1.0000000       0.7636661     0.6417821
chaotic_orderly               0.7636661       1.0000000     0.6121194
lazy_diligent                 0.6417821       0.6121194     1.0000000
tardy_on.time                 0.7893593       0.8186320     0.7435570
spontaneous_scheduled         0.8300721       0.8261965     0.5471122
underachiever_overachiever    0.5630071       0.4739749     0.7609475
                              tardy_on.time spontaneous_scheduled
messy_neat                        0.8293504             0.7805277
disorganized_self.disciplined     0.8466559             0.7413686
ADHD_OCD                          0.7893593             0.8300721
chaotic_orderly                   0.8186320             0.8261965
lazy_diligent                     0.7435570             0.5471122
tardy_on.time                     1.0000000             0.8027984
spontaneous_scheduled             0.8027984             1.0000000
underachiever_overachiever        0.6119956             0.4334656
                              underachiever_overachiever
messy_neat                                     0.5842898
disorganized_self.disciplined                  0.6923879
ADHD_OCD                                       0.5630071
chaotic_orderly                                0.4739749
lazy_diligent                                  0.7609475
tardy_on.time                                  0.6119956
spontaneous_scheduled                          0.4334656
underachiever_overachiever                     1.0000000

[1] FALSE

                                       0          1         2         3
messy_neat                    0.09223847 0.19460067 0.2080990 0.3183352
disorganized_self.disciplined 0.07761530 0.14848144 0.1799775 0.2913386
ADHD_OCD                      0.07536558 0.19572553 0.2305962 0.4004499
chaotic_orderly               0.14960630 0.23284589 0.2069741 0.2890889
lazy_diligent                 0.01912261 0.07536558 0.1282340 0.2992126
tardy_on.time                 0.07424072 0.16872891 0.2035996 0.3059618
spontaneous_scheduled         0.13948256 0.19460067 0.1766029 0.3138358
underachiever_overachiever    0.02699663 0.10461192 0.2002250 0.3948256
                                       4 miss
messy_neat                    0.18672666    0
disorganized_self.disciplined 0.30258718    0
ADHD_OCD                      0.09786277    0
chaotic_orderly               0.12148481    0
lazy_diligent                 0.47806524    0
tardy_on.time                 0.24746907    0
spontaneous_scheduled         0.17547807    0
underachiever_overachiever    0.27334083    0

....................................................
Processing Data      2024-10-06 17:27:03.507974 
    * Response Data: 889 Persons and  7 Items 
    * Numerical integration with 21 nodes
    * Created Design Matrices   ( 2024-10-06 17:27:03.510631 )
    * Calculated Sufficient Statistics   ( 2024-10-06 17:27:03.521568 )
....................................................
Iteration 1     2024-10-06 17:27:03.524478
E Step
M Step Intercepts   |----
  Deviance = 14117.3527
  Maximum item intercept parameter change: 0.349757
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.968234
....................................................
Iteration 2     2024-10-06 17:27:03.528186
E Step
M Step Intercepts   |----
  Deviance = 13676.5477 | Absolute change: 440.8049 | Relative change: 0.03223072
  Maximum item intercept parameter change: 0.41339
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.62565
....................................................
Iteration 3     2024-10-06 17:27:03.530051
E Step
M Step Intercepts   |----
  Deviance = 13529.42 | Absolute change: 147.1277 | Relative change: 0.01087465
  Maximum item intercept parameter change: 0.34842
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.558409
....................................................
Iteration 4     2024-10-06 17:27:03.713102
E Step
M Step Intercepts   |----
  Deviance = 13437.3794 | Absolute change: 92.0407 | Relative change: 0.0068496
  Maximum item intercept parameter change: 0.27763
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.491573
....................................................
Iteration 5     2024-10-06 17:27:03.715037
E Step
M Step Intercepts   |----
  Deviance = 13379.4197 | Absolute change: 57.9596 | Relative change: 0.004332
  Maximum item intercept parameter change: 0.221208
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.41836
....................................................
Iteration 6     2024-10-06 17:27:03.716833
E Step
M Step Intercepts   |----
  Deviance = 13343.2773 | Absolute change: 36.1425 | Relative change: 0.00270866
  Maximum item intercept parameter change: 0.174156
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.345819
....................................................
Iteration 7     2024-10-06 17:27:03.718567
E Step
M Step Intercepts   |----
  Deviance = 13321.0359 | Absolute change: 22.2413 | Relative change: 0.00166964
  Maximum item intercept parameter change: 0.134009
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.279501
....................................................
Iteration 8     2024-10-06 17:27:03.720322
E Step
M Step Intercepts   |----
  Deviance = 13307.4148 | Absolute change: 13.6211 | Relative change: 0.00102358
  Maximum item intercept parameter change: 0.103149
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.222651
....................................................
Iteration 9     2024-10-06 17:27:03.722051
E Step
M Step Intercepts   |----
  Deviance = 13299.1031 | Absolute change: 8.3117 | Relative change: 0.00062498
  Maximum item intercept parameter change: 0.078924
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.175285
....................................................
Iteration 10     2024-10-06 17:27:03.723792
E Step
M Step Intercepts   |----
  Deviance = 13294.0187 | Absolute change: 5.0844 | Relative change: 0.00038245
  Maximum item intercept parameter change: 0.060597
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.136884
....................................................
Iteration 11     2024-10-06 17:27:03.725503
E Step
M Step Intercepts   |----
  Deviance = 13290.8879 | Absolute change: 3.1308 | Relative change: 0.00023556
  Maximum item intercept parameter change: 0.046711
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.106331
....................................................
Iteration 12     2024-10-06 17:27:03.72721
E Step
M Step Intercepts   |----
  Deviance = 13288.9316 | Absolute change: 1.9563 | Relative change: 0.00014721
  Maximum item intercept parameter change: 0.036379
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.082384
....................................................
Iteration 13     2024-10-06 17:27:03.728909
E Step
M Step Intercepts   |----
  Deviance = 13287.6853 | Absolute change: 1.2463 | Relative change: 9.379e-05
  Maximum item intercept parameter change: 0.028624
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.063589
....................................................
Iteration 14     2024-10-06 17:27:03.730592
E Step
M Step Intercepts   |----
  Deviance = 13286.8713 | Absolute change: 0.814 | Relative change: 6.127e-05
  Maximum item intercept parameter change: 0.022698
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.049124
....................................................
Iteration 15     2024-10-06 17:27:03.732287
E Step
M Step Intercepts   |----
  Deviance = 13286.3246 | Absolute change: 0.5467 | Relative change: 4.115e-05
  Maximum item intercept parameter change: 0.018155
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.037918
....................................................
Iteration 16     2024-10-06 17:27:03.734002
E Step
M Step Intercepts   |----
  Deviance = 13285.946 | Absolute change: 0.3786 | Relative change: 2.85e-05
  Maximum item intercept parameter change: 0.014614
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.029191
....................................................
Iteration 17     2024-10-06 17:27:03.73572
E Step
M Step Intercepts   |----
  Deviance = 13285.6727 | Absolute change: 0.2733 | Relative change: 2.057e-05
  Maximum item intercept parameter change: 0.011863
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.022595
....................................................
Iteration 18     2024-10-06 17:27:03.737415
E Step
M Step Intercepts   |----
  Deviance = 13285.467 | Absolute change: 0.2056 | Relative change: 1.548e-05
  Maximum item intercept parameter change: 0.009733
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.017481
....................................................
Iteration 19     2024-10-06 17:27:03.739128
E Step
M Step Intercepts   |----
  Deviance = 13285.3074 | Absolute change: 0.1596 | Relative change: 1.202e-05
  Maximum item intercept parameter change: 0.008253
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.013624
....................................................
Iteration 20     2024-10-06 17:27:03.740835
E Step
M Step Intercepts   |----
  Deviance = 13285.1797 | Absolute change: 0.1277 | Relative change: 9.61e-06
  Maximum item intercept parameter change: 0.007094
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.010852
....................................................
Iteration 21     2024-10-06 17:27:03.742516
E Step
M Step Intercepts   |----
  Deviance = 13285.075 | Absolute change: 0.1047 | Relative change: 7.88e-06
  Maximum item intercept parameter change: 0.006166
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.008546
....................................................
Iteration 22     2024-10-06 17:27:03.74423
E Step
M Step Intercepts   |----
  Deviance = 13284.9875 | Absolute change: 0.0875 | Relative change: 6.59e-06
  Maximum item intercept parameter change: 0.005411
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.006731
....................................................
Iteration 23     2024-10-06 17:27:03.745927
E Step
M Step Intercepts   |----
  Deviance = 13284.9132 | Absolute change: 0.0743 | Relative change: 5.59e-06
  Maximum item intercept parameter change: 0.004789
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.00527
....................................................
Iteration 24     2024-10-06 17:27:03.747599
E Step
M Step Intercepts   |----
  Deviance = 13284.8495 | Absolute change: 0.0637 | Relative change: 4.8e-06
  Maximum item intercept parameter change: 0.004271
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.004155
....................................................
Iteration 25     2024-10-06 17:27:03.749297
E Step
M Step Intercepts   |----
  Deviance = 13284.7944 | Absolute change: 0.0551 | Relative change: 4.15e-06
  Maximum item intercept parameter change: 0.003837
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.003299
....................................................
Iteration 26     2024-10-06 17:27:03.750994
E Step
M Step Intercepts   |----
  Deviance = 13284.7464 | Absolute change: 0.0479 | Relative change: 3.61e-06
  Maximum item intercept parameter change: 0.00347
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.002638
....................................................
Iteration 27     2024-10-06 17:27:03.752685
E Step
M Step Intercepts   |----
  Deviance = 13284.7046 | Absolute change: 0.0418 | Relative change: 3.15e-06
  Maximum item intercept parameter change: 0.003157
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.002128
....................................................
Iteration 28     2024-10-06 17:27:03.754367
E Step
M Step Intercepts   |----
  Deviance = 13284.668 | Absolute change: 0.0366 | Relative change: 2.76e-06
  Maximum item intercept parameter change: 0.00289
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.001732
....................................................
Iteration 29     2024-10-06 17:27:03.75608
E Step
M Step Intercepts   |----
  Deviance = 13284.6358 | Absolute change: 0.0321 | Relative change: 2.42e-06
  Maximum item intercept parameter change: 0.002666
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.001424
....................................................
Iteration 30     2024-10-06 17:27:03.757769
E Step
M Step Intercepts   |----
  Deviance = 13284.6076 | Absolute change: 0.0282 | Relative change: 2.12e-06
  Maximum item intercept parameter change: 0.002467
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.001183
....................................................
Iteration 31     2024-10-06 17:27:03.759456
E Step
M Step Intercepts   |----
  Deviance = 13284.5828 | Absolute change: 0.0248 | Relative change: 1.87e-06
  Maximum item intercept parameter change: 0.002291
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000993
....................................................
Iteration 32     2024-10-06 17:27:03.761151
E Step
M Step Intercepts   |----
  Deviance = 13284.561 | Absolute change: 0.0218 | Relative change: 1.64e-06
  Maximum item intercept parameter change: 0.002138
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000843
....................................................
Iteration 33     2024-10-06 17:27:03.762855
E Step
M Step Intercepts   |----
  Deviance = 13284.5419 | Absolute change: 0.0192 | Relative change: 1.44e-06
  Maximum item intercept parameter change: 0.001997
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000723
....................................................
Iteration 34     2024-10-06 17:27:03.764548
E Step
M Step Intercepts   |----
  Deviance = 13284.525 | Absolute change: 0.0169 | Relative change: 1.27e-06
  Maximum item intercept parameter change: 0.001867
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000627
....................................................
Iteration 35     2024-10-06 17:27:03.766287
E Step
M Step Intercepts   |----
  Deviance = 13284.5101 | Absolute change: 0.0149 | Relative change: 1.12e-06
  Maximum item intercept parameter change: 0.001747
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000549
....................................................
Iteration 36     2024-10-06 17:27:03.767999
E Step
M Step Intercepts   |----
  Deviance = 13284.4971 | Absolute change: 0.0131 | Relative change: 9.8e-07
  Maximum item intercept parameter change: 0.001636
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000485
....................................................
Iteration 37     2024-10-06 17:27:03.769707
E Step
M Step Intercepts   |----
  Deviance = 13284.4855 | Absolute change: 0.0115 | Relative change: 8.7e-07
  Maximum item intercept parameter change: 0.001532
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000432
....................................................
Iteration 38     2024-10-06 17:27:03.771387
E Step
M Step Intercepts   |----
  Deviance = 13284.4754 | Absolute change: 0.0101 | Relative change: 7.6e-07
  Maximum item intercept parameter change: 0.001435
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000388
....................................................
Iteration 39     2024-10-06 17:27:03.773093
E Step
M Step Intercepts   |----
  Deviance = 13284.4665 | Absolute change: 0.0089 | Relative change: 6.7e-07
  Maximum item intercept parameter change: 0.001345
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000351
....................................................
Iteration 40     2024-10-06 17:27:03.774809
E Step
M Step Intercepts   |----
  Deviance = 13284.4586 | Absolute change: 0.0079 | Relative change: 5.9e-07
  Maximum item intercept parameter change: 0.001261
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000319
....................................................
Iteration 41     2024-10-06 17:27:03.7765
E Step
M Step Intercepts   |----
  Deviance = 13284.4517 | Absolute change: 0.0069 | Relative change: 5.2e-07
  Maximum item intercept parameter change: 0.001183
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000291
....................................................
Iteration 42     2024-10-06 17:27:03.778212
E Step
M Step Intercepts   |----
  Deviance = 13284.4456 | Absolute change: 0.0061 | Relative change: 4.6e-07
  Maximum item intercept parameter change: 0.001109
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000267
....................................................
Iteration 43     2024-10-06 17:27:03.779937
E Step
M Step Intercepts   |----
  Deviance = 13284.4402 | Absolute change: 0.0054 | Relative change: 4e-07
  Maximum item intercept parameter change: 0.00104
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000246
....................................................
Iteration 44     2024-10-06 17:27:03.781633
E Step
M Step Intercepts   |----
  Deviance = 13284.4355 | Absolute change: 0.0047 | Relative change: 3.6e-07
  Maximum item intercept parameter change: 0.000976
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000228
....................................................
Iteration 45     2024-10-06 17:27:03.783356
E Step
M Step Intercepts   |----
  Deviance = 13284.4313 | Absolute change: 0.0042 | Relative change: 3.1e-07
  Maximum item intercept parameter change: 0.000916
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000211
....................................................
Iteration 46     2024-10-06 17:27:03.785085
E Step
M Step Intercepts   |----
  Deviance = 13284.4276 | Absolute change: 0.0037 | Relative change: 2.8e-07
  Maximum item intercept parameter change: 0.000859
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000196
....................................................
Iteration 47     2024-10-06 17:27:03.78681
E Step
M Step Intercepts   |----
  Deviance = 13284.4244 | Absolute change: 0.0032 | Relative change: 2.4e-07
  Maximum item intercept parameter change: 0.000806
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000182
....................................................
Iteration 48     2024-10-06 17:27:03.788538
E Step
M Step Intercepts   |----
  Deviance = 13284.4215 | Absolute change: 0.0029 | Relative change: 2.1e-07
  Maximum item intercept parameter change: 0.000756
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.00017
....................................................
Iteration 49     2024-10-06 17:27:03.790272
E Step
M Step Intercepts   |----
  Deviance = 13284.419 | Absolute change: 0.0025 | Relative change: 1.9e-07
  Maximum item intercept parameter change: 0.00071
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000158
....................................................
Iteration 50     2024-10-06 17:27:03.791994
E Step
M Step Intercepts   |----
  Deviance = 13284.4168 | Absolute change: 0.0022 | Relative change: 1.7e-07
  Maximum item intercept parameter change: 0.000666
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000148
....................................................
Iteration 51     2024-10-06 17:27:03.793716
E Step
M Step Intercepts   |----
  Deviance = 13284.4149 | Absolute change: 0.0019 | Relative change: 1.5e-07
  Maximum item intercept parameter change: 0.000625
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000138
....................................................
Iteration 52     2024-10-06 17:27:03.795435
E Step
M Step Intercepts   |----
  Deviance = 13284.4131 | Absolute change: 0.0017 | Relative change: 1.3e-07
  Maximum item intercept parameter change: 0.000586
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000129
....................................................
Iteration 53     2024-10-06 17:27:03.797167
E Step
M Step Intercepts   |----
  Deviance = 13284.4116 | Absolute change: 0.0015 | Relative change: 1.1e-07
  Maximum item intercept parameter change: 0.00055
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000121
....................................................
Iteration 54     2024-10-06 17:27:03.798911
E Step
M Step Intercepts   |----
  Deviance = 13284.4103 | Absolute change: 0.0013 | Relative change: 1e-07
  Maximum item intercept parameter change: 0.000516
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000113
....................................................
Iteration 55     2024-10-06 17:27:03.800621
E Step
M Step Intercepts   |----
  Deviance = 13284.4091 | Absolute change: 0.0012 | Relative change: 9e-08
  Maximum item intercept parameter change: 0.000485
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000106
....................................................
Iteration 56     2024-10-06 17:27:03.802357
E Step
M Step Intercepts   |----
  Deviance = 13284.4081 | Absolute change: 0.001 | Relative change: 8e-08
  Maximum item intercept parameter change: 0.000455
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 9.9e-05
....................................................
Iteration 57     2024-10-06 17:27:03.804102
E Step
M Step Intercepts   |----
  Deviance = 13284.4072 | Absolute change: 9e-04 | Relative change: 7e-08
  Maximum item intercept parameter change: 0.000427
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 9.3e-05
....................................................
Iteration 58     2024-10-06 17:27:03.805831
E Step
M Step Intercepts   |----
  Deviance = 13284.4064 | Absolute change: 8e-04 | Relative change: 6e-08
  Maximum item intercept parameter change: 0.000401
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 8.7e-05
....................................................
Iteration 59     2024-10-06 17:27:03.807535
E Step
M Step Intercepts   |----
  Deviance = 13284.4057 | Absolute change: 7e-04 | Relative change: 5e-08
  Maximum item intercept parameter change: 0.000376
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 8.2e-05
....................................................
Iteration 60     2024-10-06 17:27:03.816386
E Step
M Step Intercepts   |----
  Deviance = 13284.405 | Absolute change: 6e-04 | Relative change: 5e-08
  Maximum item intercept parameter change: 0.000353
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 7.6e-05
....................................................
Iteration 61     2024-10-06 17:27:03.818161
E Step
M Step Intercepts   |----
  Deviance = 13284.4045 | Absolute change: 5e-04 | Relative change: 4e-08
  Maximum item intercept parameter change: 0.000331
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 7.2e-05
....................................................
Iteration 62     2024-10-06 17:27:03.819909
E Step
M Step Intercepts   |----
  Deviance = 13284.404 | Absolute change: 5e-04 | Relative change: 4e-08
  Maximum item intercept parameter change: 0.000311
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 6.7e-05
....................................................
Iteration 63     2024-10-06 17:27:03.821621
E Step
M Step Intercepts   |---
  Deviance = 13284.4036 | Absolute change: 4e-04 | Relative change: 3e-08
  Maximum item intercept parameter change: 0.000334
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 6.3e-05
....................................................
Iteration 64     2024-10-06 17:27:03.823219
E Step
M Step Intercepts   |---
  Deviance = 13284.4032 | Absolute change: 4e-04 | Relative change: 3e-08
  Maximum item intercept parameter change: 0.000293
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 7.2e-05
....................................................
Iteration 65     2024-10-06 17:27:03.824817
E Step
M Step Intercepts   |---
  Deviance = 13284.4028 | Absolute change: 4e-04 | Relative change: 3e-08
  Maximum item intercept parameter change: 0.000273
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 6.5e-05
....................................................
Iteration 66     2024-10-06 17:27:03.826413
E Step
M Step Intercepts   |---
  Deviance = 13284.4025 | Absolute change: 3e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000255
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 5.9e-05
....................................................
Iteration 67     2024-10-06 17:27:03.828025
E Step
M Step Intercepts   |---
  Deviance = 13284.4023 | Absolute change: 3e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000238
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 5.4e-05
....................................................
Iteration 68     2024-10-06 17:27:03.829621
E Step
M Step Intercepts   |---
  Deviance = 13284.402 | Absolute change: 2e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000222
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 4.9e-05
....................................................
Iteration 69     2024-10-06 17:27:03.831214
E Step
M Step Intercepts   |---
  Deviance = 13284.4018 | Absolute change: 2e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000207
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 4.5e-05
....................................................
Iteration 70     2024-10-06 17:27:03.832817
E Step
M Step Intercepts   |---
  Deviance = 13284.4016 | Absolute change: 2e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000194
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 4.2e-05
....................................................
Iteration 71     2024-10-06 17:27:03.834412
E Step
M Step Intercepts   |---
  Deviance = 13284.4015 | Absolute change: 2e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000181
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.9e-05
....................................................
Iteration 72     2024-10-06 17:27:03.836056
E Step
M Step Intercepts   |---
  Deviance = 13284.4014 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000169
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.6e-05
....................................................
Iteration 73     2024-10-06 17:27:03.837634
E Step
M Step Intercepts   |---
  Deviance = 13284.4012 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000158
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.3e-05
....................................................
Iteration 74     2024-10-06 17:27:03.839231
E Step
M Step Intercepts   |---
  Deviance = 13284.4011 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000147
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.1e-05
....................................................
Iteration 75     2024-10-06 17:27:03.840831
E Step
M Step Intercepts   |--
  Deviance = 13284.401 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000125
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 2.9e-05
....................................................
Iteration 76     2024-10-06 17:27:03.84228
E Step
M Step Intercepts   |--
  Deviance = 13284.401 | Absolute change: 1e-04 | Relative change: 0
  Maximum item intercept parameter change: 0.000107
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 1.1e-05
....................................................
Iteration 77     2024-10-06 17:27:03.843751
E Step
M Step Intercepts   |--
  Deviance = 13284.4009 | Absolute change: 1e-04 | Relative change: 0
  Maximum item intercept parameter change: 0.000101
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 1.3e-05
....................................................
Iteration 78     2024-10-06 17:27:03.845222
E Step
M Step Intercepts   |--
  Deviance = 13284.4009 | Absolute change: 1e-04 | Relative change: 0
  Maximum item intercept parameter change: 9.6e-05
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 1.5e-05
....................................................
Item Parameters
   xsi.index                          xsi.label     est
1          1 disorganized_self.disciplined_Cat1 -3.7971
2          2 disorganized_self.disciplined_Cat2 -1.7783
3          3 disorganized_self.disciplined_Cat3 -0.7349
4          4 disorganized_self.disciplined_Cat4  1.3246
5          5                      ADHD_OCD_Cat1 -3.9697
6          6                      ADHD_OCD_Cat2 -1.4140
7          7                      ADHD_OCD_Cat3 -0.1798
8          8                      ADHD_OCD_Cat4  3.7415
9          9               chaotic_orderly_Cat1 -2.6995
10        10               chaotic_orderly_Cat2 -0.5362
11        11               chaotic_orderly_Cat3  0.4170
12        12               chaotic_orderly_Cat4  3.2510
13        13                 lazy_diligent_Cat1 -5.7702
14        14                 lazy_diligent_Cat2 -3.3967
15        15                 lazy_diligent_Cat3 -2.1475
16        16                 lazy_diligent_Cat4  0.0552
17        17                 tardy_on.time_Cat1 -3.9361
18        18                 tardy_on.time_Cat2 -1.6475
19        19                 tardy_on.time_Cat3 -0.4526
20        20                 tardy_on.time_Cat4  1.8238
21        21         spontaneous_scheduled_Cat1 -2.7638
22        22         spontaneous_scheduled_Cat2 -0.8343
23        23         spontaneous_scheduled_Cat3 -0.1865
24        24         spontaneous_scheduled_Cat4  2.5848
25        25    underachiever_overachiever_Cat1 -5.4051
26        26    underachiever_overachiever_Cat2 -2.9387
27        27    underachiever_overachiever_Cat3 -1.2721
28        28    underachiever_overachiever_Cat4  1.6974
...................................
Regression Coefficients
     [,1]
[1,]    0

Variance:
      [,1]
[1,] 5.702


EAP Reliability:
[1] 0.933

-----------------------------
Start:  2024-10-06 17:27:03.507256
End:  2024-10-06 17:27:03.855042 
Time difference of 0.3477859 secs

------------------------------------------------------------
TAM 4.2-21 (2024-02-19 18:52:08) 
R version 4.4.1 (2024-06-14) x86_64, linux-gnu | nodename=fv-az1770-351 | login=unknown 

Date of Analysis: 2024-10-06 17:27:03.855042 
Time difference of 0.3477859 secs
Computation time: 0.3477859 

Multidimensional Item Response Model in TAM 

IRT Model: PCM
Call:
tam.mml(resp = psych_dat[, -1], irtmodel = "PCM")

------------------------------------------------------------
Number of iterations = 78 
Numeric integration with 21 integration points

Deviance = 13284.4 
Log likelihood = -6642.2 
Number of persons = 889 
Number of persons used = 889 
Number of items = 7 
Number of estimated parameters = 29 
    Item threshold parameters = 28 
    Item slope parameters = 0 
    Regression parameters = 0 
    Variance/covariance parameters = 1 

AIC = 13342  | penalty=58    | AIC=-2*LL + 2*p 
AIC3 = 13371  | penalty=87    | AIC3=-2*LL + 3*p 
BIC = 13481  | penalty=196.91    | BIC=-2*LL + log(n)*p 
aBIC = 13389  | penalty=104.68    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
CAIC = 13510  | penalty=225.91    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
AICc = 13344  | penalty=60.03    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
GHP = 1.07202     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 

------------------------------------------------------------
EAP Reliability
[1] 0.933
------------------------------------------------------------
Covariances and Variances
      [,1]
[1,] 5.702
------------------------------------------------------------
Correlations and Standard Deviations (in the diagonal)
      [,1]
[1,] 2.388
------------------------------------------------------------
Regression Coefficients
     [,1]
[1,]    0
------------------------------------------------------------
Item Parameters -A*Xsi
                           item   N     M xsi.item AXsi_.Cat1 AXsi_.Cat2
1 disorganized_self.disciplined 889 2.593   -1.246     -3.797     -5.575
2                      ADHD_OCD 889 2.250   -0.455     -3.970     -5.384
3               chaotic_orderly 889 2.000    0.108     -2.699     -3.236
4                 lazy_diligent 889 3.142   -2.815     -5.770     -9.167
5                 tardy_on.time 889 2.484   -1.053     -3.936     -5.584
6         spontaneous_scheduled 889 2.191   -0.300     -2.764     -3.598
7    underachiever_overachiever 889 2.783   -1.980     -5.405     -8.344
  AXsi_.Cat3 AXsi_.Cat4 B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
1     -6.310     -4.986           1           2           3           4
2     -5.563     -1.822           1           2           3           4
3     -2.819      0.432           1           2           3           4
4    -11.314    -11.259           1           2           3           4
5     -6.036     -4.212           1           2           3           4
6     -3.785     -1.200           1           2           3           4
7     -9.616     -7.919           1           2           3           4

Item Parameters Xsi
                                      xsi se.xsi
disorganized_self.disciplined_Cat1 -3.797  0.175
disorganized_self.disciplined_Cat2 -1.778  0.124
disorganized_self.disciplined_Cat3 -0.735  0.107
disorganized_self.disciplined_Cat4  1.325  0.104
ADHD_OCD_Cat1                      -3.970  0.172
ADHD_OCD_Cat2                      -1.414  0.114
ADHD_OCD_Cat3                      -0.180  0.100
ADHD_OCD_Cat4                       3.741  0.142
chaotic_orderly_Cat1               -2.699  0.133
chaotic_orderly_Cat2               -0.536  0.108
chaotic_orderly_Cat3                0.417  0.105
chaotic_orderly_Cat4                3.251  0.135
lazy_diligent_Cat1                 -5.770  0.291
lazy_diligent_Cat2                 -3.397  0.171
lazy_diligent_Cat3                 -2.147  0.121
lazy_diligent_Cat4                  0.055  0.096
tardy_on.time_Cat1                 -3.936  0.175
tardy_on.time_Cat2                 -1.647  0.119
tardy_on.time_Cat3                 -0.453  0.104
tardy_on.time_Cat4                  1.824  0.109
spontaneous_scheduled_Cat1         -2.764  0.139
spontaneous_scheduled_Cat2         -0.834  0.113
spontaneous_scheduled_Cat3         -0.187  0.105
spontaneous_scheduled_Cat4          2.585  0.119
underachiever_overachiever_Cat1    -5.405  0.254
underachiever_overachiever_Cat2    -2.939  0.145
underachiever_overachiever_Cat3    -1.272  0.105
underachiever_overachiever_Cat4     1.697  0.103

Item Parameters in IRT parameterization
                           item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3
1 disorganized_self.disciplined     1 -1.246   -2.551   -0.532    0.512
2                      ADHD_OCD     1 -0.455   -3.514   -0.959    0.276
3               chaotic_orderly     1  0.108   -2.808   -0.644    0.309
4                 lazy_diligent     1 -2.815   -2.955   -0.582    0.667
5                 tardy_on.time     1 -1.053   -2.883   -0.594    0.600
6         spontaneous_scheduled     1 -0.300   -2.464   -0.534    0.113
7    underachiever_overachiever     1 -1.980   -3.425   -0.959    0.708
  tau.Cat4
1    2.571
2    4.197
3    3.143
4    2.870
5    2.877
6    2.885
7    3.677

                                           xsi     se.xsi
disorganized_self.disciplined_Cat1 -3.79709749 0.17457941
disorganized_self.disciplined_Cat2 -1.77828685 0.12404654
disorganized_self.disciplined_Cat3 -0.73487787 0.10655057
disorganized_self.disciplined_Cat4  1.32457648 0.10390882
ADHD_OCD_Cat1                      -3.96970497 0.17206746
ADHD_OCD_Cat2                      -1.41401382 0.11376202
ADHD_OCD_Cat3                      -0.17977218 0.09962925
ADHD_OCD_Cat4                       3.74149496 0.14211581
chaotic_orderly_Cat1               -2.69946448 0.13307165
chaotic_orderly_Cat2               -0.53622820 0.10766372
chaotic_orderly_Cat3                0.41697289 0.10463369
chaotic_orderly_Cat4                3.25103731 0.13503059
lazy_diligent_Cat1                 -5.77019884 0.29142669
lazy_diligent_Cat2                 -3.39668299 0.17080254
lazy_diligent_Cat3                 -2.14749301 0.12109283
lazy_diligent_Cat4                  0.05521047 0.09558887
tardy_on.time_Cat1                 -3.93610335 0.17516854
tardy_on.time_Cat2                 -1.64749957 0.11924547
tardy_on.time_Cat3                 -0.45264211 0.10388266
tardy_on.time_Cat4                  1.82379881 0.10869816
spontaneous_scheduled_Cat1         -2.76380889 0.13870791
spontaneous_scheduled_Cat2         -0.83427238 0.11310941
spontaneous_scheduled_Cat3         -0.18654074 0.10500905
spontaneous_scheduled_Cat4          2.58478518 0.11940568
underachiever_overachiever_Cat1    -5.40509039 0.25403635
underachiever_overachiever_Cat2    -2.93873958 0.14531083
underachiever_overachiever_Cat3    -1.27212871 0.10459447
underachiever_overachiever_Cat4     1.69738710 0.10346930

character(0)

Iteration in WLE/MLE estimation  1   | Maximal change  2.0474 
Iteration in WLE/MLE estimation  2   | Maximal change  1.09 
Iteration in WLE/MLE estimation  3   | Maximal change  0.3975 
Iteration in WLE/MLE estimation  4   | Maximal change  0.0102 
Iteration in WLE/MLE estimation  5   | Maximal change  0.002 
Iteration in WLE/MLE estimation  6   | Maximal change  4e-04 
Iteration in WLE/MLE estimation  7   | Maximal change  1e-04 
----
 WLE Reliability= 0.918

Iteration in WLE/MLE estimation  1   | Maximal change  2.0474 
Iteration in WLE/MLE estimation  2   | Maximal change  1.09 
Iteration in WLE/MLE estimation  3   | Maximal change  0.3975 
Iteration in WLE/MLE estimation  4   | Maximal change  0.0102 
Iteration in WLE/MLE estimation  5   | Maximal change  0.002 
Iteration in WLE/MLE estimation  6   | Maximal change  4e-04 
Iteration in WLE/MLE estimation  7   | Maximal change  1e-04 
----
 WLE Reliability= 0.918

....................................................
 Plots exported in png format into folder:
 /home/runner/work/IRT_workshop/IRT_workshop/slides/xPL/Plots

                           item Outfit Outfit_t Outfit_p Infit Infit_t Infit_p
1 disorganized_self.disciplined   0.63    -6.18     0.00  0.66   -7.62    0.00
2                      ADHD_OCD   0.84    -3.25     0.00  0.84   -3.56    0.00
3               chaotic_orderly   0.90    -1.82     0.07  0.91   -1.92    0.05
4                 lazy_diligent   0.96    -0.29     0.77  1.01    0.26    0.80
5                 tardy_on.time   0.65    -6.76     0.00  0.67   -7.71    0.00
6         spontaneous_scheduled   1.06     1.11     0.27  1.07    1.34    0.18
7    underachiever_overachiever   1.64     9.05     0.00  1.56    9.84    0.00

**** Calculate Residuals 
**** Calculate Counts 
**** Calculate Covariances

**** Calculate Residuals 
**** Calculate Counts 
**** Calculate Covariances

     MADaQ3    maxaQ3            p
1 0.2127653 0.5200699 1.149361e-64

                           item     Group1
1 disorganized_self.disciplined 0.05481346
2                      ADHD_OCD 0.03044422
3               chaotic_orderly 0.02499056
4                 lazy_diligent 0.02921001
5                 tardy_on.time 0.06348273
6         spontaneous_scheduled 0.01908362
7    underachiever_overachiever 0.06894770


Results of PCM estimation: 

Call:  PCM(X = psych_dat) 

Conditional log-likelihood: -4387.207 
Number of iterations: 96 
Number of parameters: 31 

Item (Category) Difficulty Parameters (eta): with 0.95 CI:
                                 Estimate Std. Error lower CI upper CI
messy_neat.c2                      -0.813      0.194   -1.193   -0.432
messy_neat.c3                       1.239      0.216    0.817    1.662
messy_neat.c4                       6.087      0.269    5.558    6.615
disorganized_self.disciplined.c1   -1.960      0.193   -2.339   -1.581
disorganized_self.disciplined.c2   -1.625      0.211   -2.039   -1.210
disorganized_self.disciplined.c3   -0.175      0.224   -0.614    0.263
disorganized_self.disciplined.c4    3.485      0.256    2.983    3.987
ADHD_OCD.c1                        -2.135      0.189   -2.506   -1.765
ADHD_OCD.c2                        -1.425      0.205   -1.826   -1.024
ADHD_OCD.c3                         0.640      0.219    0.210    1.070
ADHD_OCD.c4                         6.817      0.287    6.254    7.380
chaotic_orderly.c1                 -0.677      0.140   -0.952   -0.402
chaotic_orderly.c2                  0.954      0.174    0.613    1.295
chaotic_orderly.c3                  3.657      0.214    3.237    4.076
chaotic_orderly.c4                  9.336      0.295    8.758    9.913
lazy_diligent.c1                   -4.401      0.345   -5.077   -3.725
lazy_diligent.c2                   -5.861      0.368   -6.581   -5.140
lazy_diligent.c3                   -5.889      0.353   -6.580   -5.198
lazy_diligent.c4                   -3.581      0.338   -4.242   -2.919
tardy_on.time.c1                   -2.112      0.194   -2.491   -1.733
tardy_on.time.c2                   -1.642      0.210   -2.053   -1.231
tardy_on.time.c3                    0.111      0.223   -0.326    0.548
tardy_on.time.c4                    4.297      0.261    3.785    4.809
spontaneous_scheduled.c1           -0.754      0.148   -1.044   -0.465
spontaneous_scheduled.c2            0.553      0.179    0.202    0.905
spontaneous_scheduled.c3            2.615      0.211    2.201    3.029
spontaneous_scheduled.c4            7.597      0.276    7.055    8.139
underachiever_overachiever.c1      -3.936      0.295   -4.515   -3.358
underachiever_overachiever.c2      -4.846      0.307   -5.448   -4.243
underachiever_overachiever.c3      -3.954      0.295   -4.533   -3.375
underachiever_overachiever.c4       0.084      0.298   -0.501    0.669

Item Easiness Parameters (beta) with 0.95 CI:
                                      Estimate Std. Error lower CI upper CI
beta messy_neat.c1                       1.686      0.174    1.346    2.027
beta messy_neat.c2                       0.813      0.194    0.432    1.193
beta messy_neat.c3                      -1.239      0.216   -1.662   -0.817
beta messy_neat.c4                      -6.087      0.269   -6.615   -5.558
beta disorganized_self.disciplined.c1    1.960      0.193    1.581    2.339
beta disorganized_self.disciplined.c2    1.625      0.211    1.210    2.039
beta disorganized_self.disciplined.c3    0.175      0.224   -0.263    0.614
beta disorganized_self.disciplined.c4   -3.485      0.256   -3.987   -2.983
beta ADHD_OCD.c1                         2.135      0.189    1.765    2.506
beta ADHD_OCD.c2                         1.425      0.205    1.024    1.826
beta ADHD_OCD.c3                        -0.640      0.219   -1.070   -0.210
beta ADHD_OCD.c4                        -6.817      0.287   -7.380   -6.254
beta chaotic_orderly.c1                  0.677      0.140    0.402    0.952
beta chaotic_orderly.c2                 -0.954      0.174   -1.295   -0.613
beta chaotic_orderly.c3                 -3.657      0.214   -4.076   -3.237
beta chaotic_orderly.c4                 -9.336      0.295   -9.913   -8.758
beta lazy_diligent.c1                    4.401      0.345    3.725    5.077
beta lazy_diligent.c2                    5.861      0.368    5.140    6.581
beta lazy_diligent.c3                    5.889      0.353    5.198    6.580
beta lazy_diligent.c4                    3.581      0.338    2.919    4.242
beta tardy_on.time.c1                    2.112      0.194    1.733    2.491
beta tardy_on.time.c2                    1.642      0.210    1.231    2.053
beta tardy_on.time.c3                   -0.111      0.223   -0.548    0.326
beta tardy_on.time.c4                   -4.297      0.261   -4.809   -3.785
beta spontaneous_scheduled.c1            0.754      0.148    0.465    1.044
beta spontaneous_scheduled.c2           -0.553      0.179   -0.905   -0.202
beta spontaneous_scheduled.c3           -2.615      0.211   -3.029   -2.201
beta spontaneous_scheduled.c4           -7.597      0.276   -8.139   -7.055
beta underachiever_overachiever.c1       3.936      0.295    3.358    4.515
beta underachiever_overachiever.c2       4.846      0.307    4.243    5.448
beta underachiever_overachiever.c3       3.954      0.295    3.375    4.533
beta underachiever_overachiever.c4      -0.084      0.298   -0.669    0.501


Design Matrix Block 1:
                              Location Threshold 1 Threshold 2 Threshold 3
messy_neat                     1.52164    -1.68636     0.87371     2.05193
disorganized_self.disciplined  0.87116    -1.96031     0.33549     1.44938
ADHD_OCD                       1.70425    -2.13542     0.71080     2.06417
chaotic_orderly                2.33392    -0.67674     1.63108     2.70220
lazy_diligent                 -0.89516    -4.40096    -1.45987    -0.02794
tardy_on.time                  1.07431    -2.11192     0.46992     1.75327
spontaneous_scheduled          1.89925    -0.75433     1.30753     2.06173
underachiever_overachiever     0.02106    -3.93612    -0.90950     0.89170
                              Threshold 4
messy_neat                        4.84727
disorganized_self.disciplined     3.66008
ADHD_OCD                          6.17747
chaotic_orderly                   5.67916
lazy_diligent                     2.30814
tardy_on.time                     4.18596
spontaneous_scheduled             4.98209
underachiever_overachiever        4.03816